LMFDB - Embedded newform 671.2.f.a.538.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("671.538");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.35796197563$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$60$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			538.7
Character	$\chi$	$=$	671.538
Dual form			671.2.f.a.560.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70917 - 1.70917i) q^{2} +2.11174i q^{3} +3.84252i q^{4} -0.00911084i q^{5} +(3.60931 - 3.60931i) q^{6} +(1.54773 + 1.54773i) q^{7} +(3.14918 - 3.14918i) q^{8} -1.45943 q^{9} +O(q^{10})$	\(q+(-1.70917 - 1.70917i) q^{2} +2.11174i q^{3} +3.84252i q^{4} -0.00911084i q^{5} +(3.60931 - 3.60931i) q^{6} +(1.54773 + 1.54773i) q^{7} +(3.14918 - 3.14918i) q^{8} -1.45943 q^{9} +(-0.0155720 + 0.0155720i) q^{10} +(-1.46186 - 2.97707i) q^{11} -8.11439 q^{12} -5.36148i q^{13} -5.29066i q^{14} +0.0192397 q^{15} -3.07992 q^{16} +(2.25034 - 2.25034i) q^{17} +(2.49441 + 2.49441i) q^{18} +2.30814 q^{19} +0.0350086 q^{20} +(-3.26839 + 3.26839i) q^{21} +(-2.58975 + 7.58689i) q^{22} +(1.24729 - 1.24729i) q^{23} +(6.65024 + 6.65024i) q^{24} +4.99992 q^{25} +(-9.16367 + 9.16367i) q^{26} +3.25328i q^{27} +(-5.94717 + 5.94717i) q^{28} +(-1.56937 + 1.56937i) q^{29} +(-0.0328839 - 0.0328839i) q^{30} +(3.94096 + 3.94096i) q^{31} +(-1.03425 - 1.03425i) q^{32} +(6.28679 - 3.08707i) q^{33} -7.69243 q^{34} +(0.0141011 - 0.0141011i) q^{35} -5.60788i q^{36} +(5.00505 + 5.00505i) q^{37} +(-3.94500 - 3.94500i) q^{38} +11.3220 q^{39} +(-0.0286917 - 0.0286917i) q^{40} -0.661466 q^{41} +11.1725 q^{42} +(-5.95086 + 5.95086i) q^{43} +(11.4395 - 5.61724i) q^{44} +0.0132966i q^{45} -4.26366 q^{46} +5.93807 q^{47} -6.50399i q^{48} -2.20908i q^{49} +(-8.54571 - 8.54571i) q^{50} +(4.75213 + 4.75213i) q^{51} +20.6016 q^{52} +(3.95947 - 3.95947i) q^{53} +(5.56041 - 5.56041i) q^{54} +(-0.0271236 + 0.0133188i) q^{55} +9.74815 q^{56} +4.87417i q^{57} +5.36463 q^{58} +(6.86132 + 6.86132i) q^{59} +0.0739289i q^{60} +(2.57724 + 7.37278i) q^{61} -13.4715i q^{62} +(-2.25879 - 2.25879i) q^{63} +9.69526i q^{64} -0.0488475 q^{65} +(-16.0215 - 5.46886i) q^{66} +(0.626356 + 0.626356i) q^{67} +(8.64699 + 8.64699i) q^{68} +(2.63394 + 2.63394i) q^{69} -0.0482023 q^{70} +(-9.66700 - 9.66700i) q^{71} +(-4.59600 + 4.59600i) q^{72} -7.48470i q^{73} -17.1090i q^{74} +10.5585i q^{75} +8.86906i q^{76} +(2.34513 - 6.87026i) q^{77} +(-19.3513 - 19.3513i) q^{78} +(-0.541000 - 0.541000i) q^{79} +0.0280607i q^{80} -11.2484 q^{81} +(1.13056 + 1.13056i) q^{82} +4.78874i q^{83} +(-12.5589 - 12.5589i) q^{84} +(-0.0205025 - 0.0205025i) q^{85} +20.3420 q^{86} +(-3.31409 - 3.31409i) q^{87} +(-13.9790 - 4.77167i) q^{88} +(-5.64484 - 5.64484i) q^{89} +(0.0227261 - 0.0227261i) q^{90} +(8.29811 - 8.29811i) q^{91} +(4.79273 + 4.79273i) q^{92} +(-8.32227 + 8.32227i) q^{93} +(-10.1492 - 10.1492i) q^{94} -0.0210290i q^{95} +(2.18406 - 2.18406i) q^{96} -4.16558i q^{97} +(-3.77569 + 3.77569i) q^{98} +(2.13348 + 4.34482i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 120 q^{9}+O(q^{10}) $ 120 * q - 120 * q^9	$ 120 q - 120 q^{9} - 4 q^{11} + 16 q^{12} + 16 q^{15} - 148 q^{16} + 56 q^{20} - 4 q^{22} - 4 q^{23} - 104 q^{25} + 40 q^{26} - 2 q^{33} - 8 q^{34} - 12 q^{37} + 20 q^{38} + 16 q^{42} - 10 q^{44} - 4 q^{53} + 50 q^{55} - 24 q^{56} + 64 q^{58} - 56 q^{67} + 68 q^{69} + 144 q^{70} - 12 q^{71} - 64 q^{77} + 84 q^{78} + 72 q^{81} + 40 q^{82} - 80 q^{86} + 4 q^{89} - 4 q^{91} + 4 q^{92} + 64 q^{93} + 24 q^{99}+O(q^{100}) $ 120 * q - 120 * q^9 - 4 * q^11 + 16 * q^12 + 16 * q^15 - 148 * q^16 + 56 * q^20 - 4 * q^22 - 4 * q^23 - 104 * q^25 + 40 * q^26 - 2 * q^33 - 8 * q^34 - 12 * q^37 + 20 * q^38 + 16 * q^42 - 10 * q^44 - 4 * q^53 + 50 * q^55 - 24 * q^56 + 64 * q^58 - 56 * q^67 + 68 * q^69 + 144 * q^70 - 12 * q^71 - 64 * q^77 + 84 * q^78 + 72 * q^81 + 40 * q^82 - 80 * q^86 + 4 * q^89 - 4 * q^91 + 4 * q^92 + 64 * q^93 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.70917	−	1.70917i	−1.20857	−	1.20857i	−0.971492	−	0.237074i	$-0.923812\pi$
$2$	−1.70917	−	1.70917i	−1.20857	−	1.20857i	−0.237074	−	0.971492i	$-0.576188\pi$
$3$			2.11174i			1.21921i	0.792705	+	0.609606i	$0.208672\pi$
$3$			2.11174i			1.21921i	−0.792705	+	0.609606i	$0.791328\pi$
$4$			3.84252i			1.92126i
$5$		−	0.00911084i		−	0.00407449i	−0.999998	−	0.00203724i	$-0.999352\pi$
$5$		−	0.00911084i		−	0.00407449i	0.999998	−	0.00203724i	$-0.000648476\pi$
$6$	3.60931	−	3.60931i	1.47350	−	1.47350i
$7$	1.54773	+	1.54773i	0.584986	+	0.584986i	0.936269	−	0.351283i	$-0.114255\pi$
$7$	1.54773	+	1.54773i	0.584986	+	0.584986i	−0.351283	+	0.936269i	$0.614255\pi$
$8$	3.14918	−	3.14918i	1.11340	−	1.11340i
$9$	−1.45943			−0.486476
$10$	−0.0155720	+	0.0155720i	−0.00492429	+	0.00492429i
$11$	−1.46186	−	2.97707i	−0.440768	−	0.897621i
$11$	−1.46186	−	2.97707i	−0.440768	−	0.897621i
$12$	−8.11439			−2.34242
$13$		−	5.36148i		−	1.48701i	−0.668732	−	0.743503i	$-0.733163\pi$
$13$		−	5.36148i		−	1.48701i	0.668732	−	0.743503i	$-0.266837\pi$
$14$		−	5.29066i		−	1.41399i
$15$	0.0192397			0.00496766
$16$	−3.07992			−0.769981
$17$	2.25034	−	2.25034i	0.545788	−	0.545788i	−0.379432	−	0.925220i	$-0.623880\pi$
$17$	2.25034	−	2.25034i	0.545788	−	0.545788i	0.925220	+	0.379432i	$0.123880\pi$
$18$	2.49441	+	2.49441i	0.587938	+	0.587938i
$19$	2.30814			0.529523			0.264761	−	0.964314i	$-0.414707\pi$
$19$	2.30814			0.529523			0.264761	+	0.964314i	$0.414707\pi$
$20$	0.0350086			0.00782816
$21$	−3.26839	+	3.26839i	−0.713221	+	0.713221i
$22$	−2.58975	+	7.58689i	−0.552136	+	1.61753i
$23$	1.24729	−	1.24729i	0.260078	−	0.260078i	−0.565008	−	0.825086i	$-0.691127\pi$
$23$	1.24729	−	1.24729i	0.260078	−	0.260078i	0.825086	+	0.565008i	$0.191127\pi$
$24$	6.65024	+	6.65024i	1.35747	+	1.35747i
$25$	4.99992			0.999983
$26$	−9.16367	+	9.16367i	−1.79714	+	1.79714i
$27$			3.25328i			0.626095i
$28$	−5.94717	+	5.94717i	−1.12391	+	1.12391i
$29$	−1.56937	+	1.56937i	−0.291424	+	0.291424i	−0.837643	−	0.546218i	$-0.816067\pi$
$29$	−1.56937	+	1.56937i	−0.291424	+	0.291424i	0.546218	+	0.837643i	$0.316067\pi$
$30$	−0.0328839	−	0.0328839i	−0.00600375	−	0.00600375i
$31$	3.94096	+	3.94096i	0.707817	+	0.707817i	0.966076	−	0.258258i	$-0.0831486\pi$
$31$	3.94096	+	3.94096i	0.707817	+	0.707817i	−0.258258	+	0.966076i	$0.583149\pi$
$32$	−1.03425	−	1.03425i	−0.182831	−	0.182831i
$33$	6.28679	−	3.08707i	1.09439	−	0.537390i
$34$	−7.69243			−1.31924
$35$	0.0141011	−	0.0141011i	0.00238352	−	0.00238352i
$36$		−	5.60788i		−	0.934646i
$37$	5.00505	+	5.00505i	0.822825	+	0.822825i	0.986512	−	0.163687i	$-0.0523387\pi$
$37$	5.00505	+	5.00505i	0.822825	+	0.822825i	−0.163687	+	0.986512i	$0.552339\pi$
$38$	−3.94500	−	3.94500i	−0.639963	−	0.639963i
$39$	11.3220			1.81297
$40$	−0.0286917	−	0.0286917i	−0.00453655	−	0.00453655i
$41$	−0.661466			−0.103304			−0.0516518	−	0.998665i	$-0.516449\pi$
$41$	−0.661466			−0.103304			−0.0516518	+	0.998665i	$0.516449\pi$
$42$	11.1725			1.72395
$43$	−5.95086	+	5.95086i	−0.907497	+	0.907497i	−0.996070	−	0.0885725i	$-0.971770\pi$
$43$	−5.95086	+	5.95086i	−0.907497	+	0.907497i	0.0885725	+	0.996070i	$0.471770\pi$
$44$	11.4395	−	5.61724i	1.72456	−	0.846831i
$45$			0.0132966i			0.00198214i
$46$	−4.26366			−0.628642
$47$	5.93807			0.866157			0.433078	−	0.901356i	$-0.357427\pi$
$47$	5.93807			0.866157			0.433078	+	0.901356i	$0.357427\pi$
$48$		−	6.50399i		−	0.938769i
$49$		−	2.20908i		−	0.315583i
$50$	−8.54571	−	8.54571i	−1.20855	−	1.20855i
$51$	4.75213	+	4.75213i	0.665431	+	0.665431i
$52$	20.6016			2.85693
$53$	3.95947	−	3.95947i	0.543875	−	0.543875i	−0.380788	−	0.924662i	$-0.624347\pi$
$53$	3.95947	−	3.95947i	0.543875	−	0.543875i	0.924662	+	0.380788i	$0.124347\pi$
$54$	5.56041	−	5.56041i	0.756676	−	0.756676i
$55$	−0.0271236	+	0.0133188i	−0.00365735	+	0.00179591i
$56$	9.74815			1.30265
$57$			4.87417i			0.645600i
$58$	5.36463			0.704411
$59$	6.86132	+	6.86132i	0.893268	+	0.893268i	0.994829	−	0.101561i	$-0.0323838\pi$
$59$	6.86132	+	6.86132i	0.893268	+	0.893268i	−0.101561	+	0.994829i	$0.532384\pi$
$60$			0.0739289i			0.00954417i
$61$	2.57724	+	7.37278i	0.329982	+	0.943987i
$61$	2.57724	+	7.37278i	0.329982	+	0.943987i
$62$		−	13.4715i		−	1.71089i
$63$	−2.25879	−	2.25879i	−0.284581	−	0.284581i
$64$			9.69526i			1.21191i
$65$	−0.0488475			−0.00605879
$66$	−16.0215	−	5.46886i	−1.97211	−	0.673171i
$67$	0.626356	+	0.626356i	0.0765215	+	0.0765215i	0.744332	−	0.667810i	$-0.232768\pi$
$67$	0.626356	+	0.626356i	0.0765215	+	0.0765215i	−0.667810	+	0.744332i	$0.732768\pi$
$68$	8.64699	+	8.64699i	1.04860	+	1.04860i
$69$	2.63394	+	2.63394i	0.317090	+	0.317090i
$70$	−0.0482023			−0.00576128
$71$	−9.66700	−	9.66700i	−1.14726	−	1.14726i	−0.987089	−	0.160173i	$-0.948795\pi$
$71$	−9.66700	−	9.66700i	−1.14726	−	1.14726i	−0.160173	−	0.987089i	$-0.551205\pi$
$72$	−4.59600	+	4.59600i	−0.541644	+	0.541644i
$73$		−	7.48470i		−	0.876017i	−0.898971	−	0.438009i	$-0.855684\pi$
$73$		−	7.48470i		−	0.876017i	0.898971	−	0.438009i	$-0.144316\pi$
$74$		−	17.1090i		−	1.98888i
$75$			10.5585i			1.21919i
$76$			8.86906i			1.01735i
$77$	2.34513	−	6.87026i	0.267252	−	0.782939i
$78$	−19.3513	−	19.3513i	−2.19110	−	2.19110i
$79$	−0.541000	−	0.541000i	−0.0608672	−	0.0608672i	0.676018	−	0.736885i	$-0.263704\pi$
$79$	−0.541000	−	0.541000i	−0.0608672	−	0.0608672i	−0.736885	+	0.676018i	$0.763704\pi$
$80$			0.0280607i			0.00313728i
$81$	−11.2484			−1.24982
$82$	1.13056	+	1.13056i	0.124849	+	0.124849i
$83$			4.78874i			0.525633i	0.964846	+	0.262816i	$0.0846514\pi$
$83$			4.78874i			0.525633i	−0.964846	+	0.262816i	$0.915349\pi$
$84$	−12.5589	−	12.5589i	−1.37028	−	1.37028i
$85$	−0.0205025	−	0.0205025i	−0.00222381	−	0.00222381i
$86$	20.3420			2.19354
$87$	−3.31409	−	3.31409i	−0.355308	−	0.355308i
$88$	−13.9790	−	4.77167i	−1.49017	−	0.508661i
$89$	−5.64484	−	5.64484i	−0.598352	−	0.598352i	0.341522	−	0.939874i	$-0.389058\pi$
$89$	−5.64484	−	5.64484i	−0.598352	−	0.598352i	−0.939874	+	0.341522i	$0.889058\pi$
$90$	0.0227261	−	0.0227261i	0.00239555	−	0.00239555i
$91$	8.29811	−	8.29811i	0.869878	−	0.869878i
$92$	4.79273	+	4.79273i	0.499677	+	0.499677i
$93$	−8.32227	+	8.32227i	−0.862979	+	0.862979i
$94$	−10.1492	−	10.1492i	−1.04681	−	1.04681i
$95$		−	0.0210290i		−	0.00215753i
$96$	2.18406	−	2.18406i	0.222909	−	0.222909i
$97$		−	4.16558i		−	0.422950i	−0.977383	−	0.211475i	$-0.932173\pi$
$97$		−	4.16558i		−	0.422950i	0.977383	−	0.211475i	$-0.0678268\pi$
$98$	−3.77569	+	3.77569i	−0.381402	+	0.381402i
$99$	2.13348	+	4.34482i	0.214423	+	0.436671i
$100$			19.2123i			1.92123i
$101$	−2.66627	−	2.66627i	−0.265304	−	0.265304i	0.561901	−	0.827205i	$-0.310070\pi$
$101$	−2.66627	−	2.66627i	−0.265304	−	0.265304i	−0.827205	+	0.561901i	$0.810070\pi$
$102$		−	16.2444i		−	1.60843i
$103$	−8.82978			−0.870024			−0.435012	−	0.900425i	$-0.643256\pi$
$103$	−8.82978			−0.870024			−0.435012	+	0.900425i	$0.643256\pi$
$104$	−16.8843	−	16.8843i	−1.65564	−	1.65564i
$105$	0.0297778	+	0.0297778i	0.00290601	+	0.00290601i
$106$	−13.5348			−1.31462
$107$	18.2306			1.76242			0.881210	−	0.472725i	$-0.156730\pi$
$107$	18.2306			1.76242			0.881210	+	0.472725i	$0.156730\pi$
$108$	−12.5008			−1.20289
$109$	11.5490			1.10619			0.553096	−	0.833117i	$-0.313446\pi$
$109$	11.5490			1.10619			0.553096	+	0.833117i	$0.313446\pi$
$110$	0.0691229	+	0.0235948i	0.00659061	+	0.00224967i
$111$	−10.5693	+	10.5693i	−1.00320	+	1.00320i
$112$	−4.76688	−	4.76688i	−0.450428	−	0.450428i
$113$		−	1.10454i		−	0.103906i	−0.998650	−	0.0519530i	$-0.983455\pi$
$113$		−	1.10454i		−	0.103906i	0.998650	−	0.0519530i	$-0.0165446\pi$
$114$	8.33079	−	8.33079i	0.780250	−	0.780250i
$115$	−0.0113638	−	0.0113638i	−0.00105968	−	0.00105968i
$116$	−6.03033	−	6.03033i	−0.559902	−	0.559902i
$117$			7.82468i			0.723392i
$118$		−	23.4543i		−	2.15915i
$119$	6.96583			0.638557
$120$	0.0605892	−	0.0605892i	0.00553101	−	0.00553101i
$121$	−6.72591	+	8.70414i	−0.611447	+	0.791286i
$122$	8.19638	−	17.0063i	0.742066	−	1.53968i
$123$		−	1.39684i		−	0.125949i
$124$	−15.1432	+	15.1432i	−1.35990	+	1.35990i
$125$		−	0.0911076i		−	0.00814891i
$126$			7.72133i			0.687870i
$127$	11.9925			1.06416			0.532082	−	0.846693i	$-0.321410\pi$
$127$	11.9925			1.06416			0.532082	+	0.846693i	$0.321410\pi$
$128$	14.5023	−	14.5023i	1.28184	−	1.28184i
$129$	−12.5666	−	12.5666i	−1.10643	−	1.10643i
$130$	0.0834887	+	0.0834887i	0.00732245	+	0.00732245i
$131$			21.3347i			1.86403i	0.362426	+	0.932013i	$0.381949\pi$
$131$			21.3347i			1.86403i	−0.362426	+	0.932013i	$0.618051\pi$
$132$	11.8621	+	24.1571i	1.03247	+	2.10261i
$133$	3.57237	+	3.57237i	0.309763	+	0.309763i
$134$		−	2.14110i		−	0.184962i
$135$	0.0296401			0.00255102
$136$		−	14.1735i		−	1.21536i
$137$	20.4458			1.74681			0.873403	−	0.486999i	$-0.161908\pi$
$137$	20.4458			1.74681			0.873403	+	0.486999i	$0.161908\pi$
$138$		−	9.00372i		−	0.766447i
$139$	−7.22067	+	7.22067i	−0.612449	+	0.612449i	−0.943584	−	0.331135i	$-0.892569\pi$
$139$	−7.22067	+	7.22067i	−0.612449	+	0.612449i	0.331135	+	0.943584i	$0.392569\pi$
$140$	0.0541837	+	0.0541837i	0.00457936	+	0.00457936i
$141$			12.5396i			1.05603i
$142$			33.0451i			2.77308i
$143$	−15.9615	+	7.83775i	−1.33477	+	0.655425i
$144$	4.49492			0.374577
$145$	0.0142983	+	0.0142983i	0.00118741	+	0.00118741i
$146$	−12.7926	+	12.7926i	−1.05872	+	1.05872i
$147$	4.66499			0.384762
$148$	−19.2320	+	19.2320i	−1.58086	+	1.58086i
$149$	−12.2128			−1.00051			−0.500255	−	0.865878i	$-0.666761\pi$
$149$	−12.2128			−1.00051			−0.500255	+	0.865878i	$0.666761\pi$
$150$	18.0463	−	18.0463i	1.47347	−	1.47347i
$151$	−3.03241	+	3.03241i	−0.246774	+	0.246774i	−0.819645	−	0.572871i	$-0.805830\pi$
$151$	−3.03241	+	3.03241i	−0.246774	+	0.246774i	0.572871	+	0.819645i	$0.305830\pi$
$152$	7.26874	−	7.26874i	0.589572	−	0.589572i
$153$	−3.28421	+	3.28421i	−0.265513	+	0.265513i
$154$	−15.7507	+	7.73422i	−1.26922	+	0.623241i
$155$	0.0359054	−	0.0359054i	0.00288399	−	0.00288399i
$156$			43.5051i			3.48320i
$157$	−2.47693	−	2.47693i	−0.197681	−	0.197681i	0.601324	−	0.799005i	$-0.294640\pi$
$157$	−2.47693	−	2.47693i	−0.197681	−	0.197681i	−0.799005	+	0.601324i	$0.794640\pi$
$158$			1.84932i			0.147124i
$159$	8.36135	+	8.36135i	0.663098	+	0.663098i
$160$	−0.00942286	+	0.00942286i	−0.000744943	+	0.000744943i
$161$	3.86093			0.304284
$162$	19.2253	+	19.2253i	1.51049	+	1.51049i
$163$		−	16.7667i		−	1.31327i	−0.754209	−	0.656635i	$-0.771979\pi$
$163$		−	16.7667i		−	1.31327i	0.754209	−	0.656635i	$-0.228021\pi$
$164$		−	2.54170i		−	0.198473i
$165$	−0.0281258	−	0.0572779i	−0.00218959	−	0.00445908i
$166$	8.18477	−	8.18477i	0.635262	−	0.635262i
$167$	4.71077			0.364530			0.182265	−	0.983249i	$-0.441657\pi$
$167$	4.71077			0.364530			0.182265	+	0.983249i	$0.441657\pi$
$168$			20.5855i			1.58821i
$169$	−15.7454			−1.21119
$170$			0.0700845i			0.00537523i
$171$	−3.36856			−0.257600
$172$	−22.8663	−	22.8663i	−1.74354	−	1.74354i
$173$	−5.76549	−	5.76549i	−0.438342	−	0.438342i	0.453111	−	0.891454i	$-0.350314\pi$
$173$	−5.76549	−	5.76549i	−0.438342	−	0.438342i	−0.891454	+	0.453111i	$0.850314\pi$
$174$			11.3287i			0.858825i
$175$	7.73851	+	7.73851i	0.584976	+	0.584976i
$176$	4.50243	+	9.16916i	0.339383	+	0.691151i
$177$	−14.4893	+	14.4893i	−1.08908	+	1.08908i
$178$			19.2960i			1.44629i
$179$	14.6949			1.09835			0.549175	−	0.835707i	$-0.314942\pi$
$179$	14.6949			1.09835			0.549175	+	0.835707i	$0.314942\pi$
$180$	−0.0510925			−0.00380821
$181$	6.53624	+	6.53624i	0.485835	+	0.485835i	0.906989	−	0.421154i	$-0.138375\pi$
$181$	6.53624	+	6.53624i	0.485835	+	0.485835i	−0.421154	+	0.906989i	$0.638375\pi$
$182$	−28.3657			−2.10261
$183$	−15.5694	+	5.44245i	−1.15092	+	0.402318i
$184$		−	7.85588i		−	0.579143i
$185$	0.0456002	−	0.0456002i	0.00335259	−	0.00335259i
$186$	28.4483			2.08593
$187$	−9.98912	−	3.40974i	−0.730477	−	0.249345i
$188$			22.8172i			1.66411i
$189$	−5.03520	+	5.03520i	−0.366257	+	0.366257i
$190$	−0.0359422	+	0.0359422i	−0.00260752	+	0.00260752i
$191$	−5.98696	−	5.98696i	−0.433201	−	0.433201i	0.456515	−	0.889716i	$-0.349098\pi$
$191$	−5.98696	−	5.98696i	−0.433201	−	0.433201i	−0.889716	+	0.456515i	$0.849098\pi$
$192$	−20.4738			−1.47757
$193$	6.99460	−	6.99460i	0.503483	−	0.503483i	−0.409036	−	0.912518i	$-0.634135\pi$
$193$	6.99460	−	6.99460i	0.503483	−	0.503483i	0.912518	+	0.409036i	$0.134135\pi$
$194$	−7.11968	+	7.11968i	−0.511163	+	0.511163i
$195$		−	0.103153i		−	0.00738695i
$196$	8.48844			0.606317
$197$	−3.07986			−0.219431			−0.109716	−	0.993963i	$-0.534994\pi$
$197$	−3.07986			−0.219431			−0.109716	+	0.993963i	$0.534994\pi$
$198$	3.77955	−	11.0725i	0.268601	−	0.786889i
$199$	−7.31244			−0.518365			−0.259183	−	0.965828i	$-0.583453\pi$
$199$	−7.31244			−0.518365			−0.259183	+	0.965828i	$0.583453\pi$
$200$	15.7456	−	15.7456i	1.11338	−	1.11338i
$201$	−1.32270	+	1.32270i	−0.0932959	+	0.0932959i
$202$			9.11422i			0.641274i
$203$	−4.85791			−0.340958
$204$	−18.2601	+	18.2601i	−1.27847	+	1.27847i
$205$			0.00602651i			0.000420910i
$206$	15.0916	+	15.0916i	1.05148	+	1.05148i
$207$	−1.82033	+	1.82033i	−0.126521	+	0.126521i
$208$			16.5129i			1.14497i
$209$	−3.37418	−	6.87149i	−0.233397	−	0.475311i
$210$		−	0.101791i		−	0.00702421i
$211$	7.96320	−	7.96320i	0.548209	−	0.548209i	−0.377713	−	0.925923i	$-0.623289\pi$
$211$	7.96320	−	7.96320i	0.548209	−	0.548209i	0.925923	+	0.377713i	$0.123289\pi$
$212$	15.2143	+	15.2143i	1.04492	+	1.04492i
$213$	20.4142	−	20.4142i	1.39875	−	1.39875i
$214$	−31.1592	−	31.1592i	−2.13000	−	2.13000i
$215$	0.0542173	+	0.0542173i	0.00369759	+	0.00369759i
$216$	10.2452	+	10.2452i	0.697096	+	0.697096i
$217$			12.1991i			0.828127i
$218$	−19.7392	−	19.7392i	−1.33691	−	1.33691i
$219$	15.8057			1.06805
$220$	−0.0511777	−	0.104223i	−0.00345040	−	0.00702672i
$221$	−12.0652	−	12.0652i	−0.811590	−	0.811590i
$222$	36.1296			2.42486
$223$	18.2299	−	18.2299i	1.22076	−	1.22076i	0.253402	−	0.967361i	$-0.418451\pi$
$223$	18.2299	−	18.2299i	1.22076	−	1.22076i	0.967361	−	0.253402i	$-0.0815495\pi$
$224$		−	3.20147i		−	0.213907i
$225$	−7.29701			−0.486468
$226$	−1.88784	+	1.88784i	−0.125577	+	0.125577i
$227$	−6.66856	−	6.66856i	−0.442608	−	0.442608i	0.450280	−	0.892887i	$-0.351324\pi$
$227$	−6.66856	−	6.66856i	−0.442608	−	0.442608i	−0.892887	+	0.450280i	$0.851324\pi$
$228$	−18.7291			−1.24037
$229$			22.1136i			1.46131i	0.682749	+	0.730653i	$0.260784\pi$
$229$			22.1136i			1.46131i	−0.682749	+	0.730653i	$0.739216\pi$
$230$			0.0388455i			0.00256139i
$231$	14.5082	+	4.95229i	0.954568	+	0.325837i
$232$			9.88445i			0.648946i
$233$	−16.0609	−	16.0609i	−1.05218	−	1.05218i	−0.998561	−	0.0536235i	$-0.982923\pi$
$233$	−16.0609	−	16.0609i	−1.05218	−	1.05218i	−0.0536235	−	0.998561i	$-0.517077\pi$
$234$	13.3737	−	13.3737i	0.874267	−	0.874267i
$235$		−	0.0541008i		−	0.00352915i
$236$	−26.3648	+	26.3648i	−1.71620	+	1.71620i
$237$	1.14245	−	1.14245i	0.0742100	−	0.0742100i
$238$	−11.9058	−	11.9058i	−0.771738	−	0.771738i
$239$			18.4145i			1.19114i	0.803305	+	0.595568i	$0.203073\pi$
$239$			18.4145i			1.19114i	−0.803305	+	0.595568i	$0.796927\pi$
$240$	−0.0592567			−0.00382501
$241$		−	7.30306i		−	0.470431i	−0.971943	−	0.235216i	$-0.924420\pi$
$241$		−	7.30306i		−	0.470431i	0.971943	−	0.235216i	$-0.0755797\pi$
$242$	26.3726	−	3.38113i	1.69529	−	0.217347i
$243$		−	13.9937i		−	0.897696i
$244$	−28.3300	+	9.90310i	−1.81365	+	0.633981i
$245$	−0.0201266			−0.00128584
$246$	−2.38744	+	2.38744i	−0.152218	+	0.152218i
$247$		−	12.3750i		−	0.787404i
$248$	24.8216			1.57617
$249$	−10.1126			−0.640857
$250$	−0.155718	+	0.155718i	−0.00984849	+	0.00984849i
$251$	1.57553	−	1.57553i	0.0994467	−	0.0994467i	−0.655633	−	0.755080i	$-0.727598\pi$
$251$	1.57553	−	1.57553i	0.0994467	−	0.0994467i	0.755080	+	0.655633i	$0.227598\pi$
$252$	8.67947	−	8.67947i	0.546755	−	0.546755i
$253$	−5.53663	−	1.88990i	−0.348085	−	0.118817i
$254$	−20.4972	−	20.4972i	−1.28611	−	1.28611i
$255$	0.0432959	−	0.0432959i	0.00271129	−	0.00271129i
$256$	−30.1834			−1.88646
$257$	−10.7464			−0.670345			−0.335172	−	0.942157i	$-0.608795\pi$
$257$	−10.7464			−0.670345			−0.335172	+	0.942157i	$0.608795\pi$
$258$			42.9570i			2.67439i
$259$			15.4929i			0.962683i
$260$		−	0.187698i		−	0.0116405i
$261$	2.29038	−	2.29038i	0.141771	−	0.141771i
$262$	36.4647	−	36.4647i	2.25280	−	2.25280i
$263$	11.4411			0.705489			0.352745	−	0.935720i	$-0.385248\pi$
$263$	11.4411			0.705489			0.352745	+	0.935720i	$0.385248\pi$
$264$	10.0765	−	29.5200i	0.620165	−	1.81683i
$265$	−0.0360741	−	0.0360741i	−0.00221601	−	0.00221601i
$266$		−	12.2116i		−	0.748739i
$267$	11.9204	−	11.9204i	0.729517	−	0.729517i
$268$	−2.40678	+	2.40678i	−0.147018	+	0.147018i
$269$	−5.36874			−0.327338			−0.163669	−	0.986515i	$-0.552333\pi$
$269$	−5.36874			−0.327338			−0.163669	+	0.986515i	$0.552333\pi$
$270$	−0.0506600	−	0.0506600i	−0.00308307	−	0.00308307i
$271$	16.7420			1.01701			0.508503	−	0.861060i	$-0.330199\pi$
$271$	16.7420			1.01701			0.508503	+	0.861060i	$0.330199\pi$
$272$	−6.93088	+	6.93088i	−0.420247	+	0.420247i
$273$	17.5234	+	17.5234i	1.06056	+	1.06056i
$274$	−34.9454	−	34.9454i	−2.11113	−	2.11113i
$275$	−7.30919	−	14.8851i	−0.440761	−	0.897606i
$276$	−10.1210	+	10.1210i	−0.609212	+	0.609212i
$277$	−12.9868	−	12.9868i	−0.780300	−	0.780300i	0.199581	−	0.979881i	$-0.436042\pi$
$277$	−12.9868	−	12.9868i	−0.780300	−	0.780300i	−0.979881	+	0.199581i	$0.936042\pi$
$278$	24.6827			1.48037
$279$	−5.75154	−	5.75154i	−0.344336	−	0.344336i
$280$		−	0.0888137i		−	0.00530764i
$281$	−4.21805	+	4.21805i	−0.251628	+	0.251628i	−0.821638	−	0.570010i	$-0.806939\pi$
$281$	−4.21805	+	4.21805i	−0.251628	+	0.251628i	0.570010	+	0.821638i	$0.306939\pi$
$282$	21.4324	−	21.4324i	1.27628	−	1.27628i
$283$	−30.4626			−1.81081			−0.905406	−	0.424547i	$-0.860433\pi$
$283$	−30.4626			−1.81081			−0.905406	+	0.424547i	$0.860433\pi$
$284$	37.1457	−	37.1457i	2.20419	−	2.20419i
$285$	0.0444078			0.00263049
$286$	40.6770	+	13.8849i	2.40528	+	0.821030i
$287$	−1.02377	−	1.02377i	−0.0604312	−	0.0604312i
$288$	1.50941	+	1.50941i	0.0889428	+	0.0889428i
$289$			6.87192i			0.404231i
$290$		−	0.0488763i		−	0.00287011i
$291$	8.79660			0.515666
$292$	28.7601			1.68306
$293$	−2.70515			−0.158037			−0.0790183	−	0.996873i	$-0.525179\pi$
$293$	−2.70515			−0.158037			−0.0790183	+	0.996873i	$0.525179\pi$
$294$	−7.97326	−	7.97326i	−0.465010	−	0.465010i
$295$	0.0625124	−	0.0625124i	0.00363961	−	0.00363961i
$296$	31.5236			1.83227
$297$	9.68526	−	4.75585i	0.561996	−	0.275963i
$298$	20.8737	+	20.8737i	1.20918	+	1.20918i
$299$	−6.68731	−	6.68731i	−0.386737	−	0.386737i
$300$	−40.5713			−2.34238
$301$	−18.4206			−1.06175
$302$	10.3658			0.596486
$303$	5.63046	−	5.63046i	0.323461	−	0.323461i
$304$	−7.10888			−0.407722
$305$	0.0671722	−	0.0234808i	0.00384627	−	0.00134451i
$306$	11.2265			0.641779
$307$	−21.3747	−	21.3747i	−1.21992	−	1.21992i	−0.967661	−	0.252255i	$-0.918828\pi$
$307$	−21.3747	−	21.3747i	−1.21992	−	1.21992i	−0.252255	−	0.967661i	$-0.581172\pi$
$308$	26.3991	+	9.01121i	1.50423	+	0.513461i
$309$		−	18.6462i		−	1.06074i
$310$	−0.122737			−0.00697099
$311$	−6.82470	−	6.82470i	−0.386993	−	0.386993i	0.486620	−	0.873614i	$-0.338230\pi$
$311$	−6.82470	−	6.82470i	−0.386993	−	0.386993i	−0.873614	+	0.486620i	$0.838230\pi$
$312$	35.6551	−	35.6551i	2.01857	−	2.01857i
$313$	−16.8537	−	16.8537i	−0.952626	−	0.952626i	0.0463019	−	0.998927i	$-0.485256\pi$
$313$	−16.8537	−	16.8537i	−0.952626	−	0.952626i	−0.998927	+	0.0463019i	$0.985256\pi$
$314$			8.46700i			0.477820i
$315$	−0.0205795	+	0.0205795i	−0.00115952	+	0.00115952i
$316$	2.07880	−	2.07880i	0.116942	−	0.116942i
$317$	8.10218			0.455064			0.227532	−	0.973771i	$-0.426934\pi$
$317$	8.10218			0.455064			0.227532	+	0.973771i	$0.426934\pi$
$318$		−	28.5819i		−	1.60279i
$319$	6.96632	+	2.37792i	0.390039	+	0.133138i
$320$	0.0883319			0.00493790
$321$			38.4982i			2.14876i
$322$	−6.59898	−	6.59898i	−0.367747	−	0.367747i
$323$	5.19410	−	5.19410i	0.289007	−	0.289007i
$324$		−	43.2220i		−	2.40122i
$325$		−	26.8069i		−	1.48698i
$326$	−28.6571	+	28.6571i	−1.58717	+	1.58717i
$327$			24.3884i			1.34868i
$328$	−2.08308	+	2.08308i	−0.115019	+	0.115019i
$329$	9.19051	+	9.19051i	0.506689	+	0.506689i
$330$	−0.0498259	+	0.145969i	−0.00274283	+	0.00803535i
$331$	−17.3418	+	17.3418i	−0.953192	+	0.953192i	−0.998952	−	0.0457608i	$-0.985429\pi$
$331$	−17.3418	+	17.3418i	−0.953192	+	0.953192i	0.0457608	+	0.998952i	$0.485429\pi$
$332$	−18.4008			−1.00988
$333$	−7.30451	−	7.30451i	−0.400284	−	0.400284i
$334$	−8.05150	−	8.05150i	−0.440558	−	0.440558i
$335$	0.00570662	−	0.00570662i	0.000311786	−	0.000311786i
$336$	10.0664	−	10.0664i	0.549167	−	0.549167i
$337$	1.15435	+	1.15435i	0.0628816	+	0.0628816i	0.737848	−	0.674967i	$-0.235842\pi$
$337$	1.15435	+	1.15435i	0.0628816	+	0.0628816i	−0.674967	+	0.737848i	$0.735842\pi$
$338$	26.9116	+	26.9116i	1.46380	+	1.46380i
$339$	2.33249			0.126683
$340$	0.0787813	−	0.0787813i	0.00427251	−	0.00427251i
$341$	5.97138	−	17.4937i	0.323368	−	0.947335i
$342$	5.75743	+	5.75743i	0.311326	+	0.311326i
$343$	14.2531	−	14.2531i	0.769597	−	0.769597i
$344$			37.4806i			2.02082i
$345$	0.0239974	−	0.0239974i	0.00129198	−	0.00129198i
$346$			19.7084i			1.05953i
$347$			27.3364i			1.46749i	0.679423	+	0.733747i	$0.262230\pi$
$347$			27.3364i			1.46749i	−0.679423	+	0.733747i	$0.737770\pi$
$348$	12.7345	−	12.7345i	0.682639	−	0.682639i
$349$	−3.40712	−	3.40712i	−0.182379	−	0.182379i	0.610013	−	0.792392i	$-0.291164\pi$
$349$	−3.40712	−	3.40712i	−0.182379	−	0.182379i	−0.792392	+	0.610013i	$0.791164\pi$
$350$		−	26.4528i		−	1.41396i
$351$	17.4424			0.931007
$352$	−1.56710	+	4.59096i	−0.0835268	+	0.244699i
$353$		−	6.01814i		−	0.320313i	−0.987092	−	0.160157i	$-0.948800\pi$
$353$		−	6.01814i		−	0.320313i	0.987092	−	0.160157i	$-0.0511999\pi$
$354$	49.5293			2.63245
$355$	−0.0880745	+	0.0880745i	−0.00467451	+	0.00467451i
$356$	21.6904	−	21.6904i	1.14959	−	1.14959i
$357$			14.7100i			0.778535i
$358$	−25.1161	−	25.1161i	−1.32743	−	1.32743i
$359$	−11.1923	+	11.1923i	−0.590708	+	0.590708i	−0.937823	−	0.347114i	$-0.887162\pi$
$359$	−11.1923	+	11.1923i	−0.590708	+	0.590708i	0.347114	+	0.937823i	$0.387162\pi$
$360$	0.0418734	+	0.0418734i	0.00220692	+	0.00220692i
$361$	−13.6725			−0.719606
$362$		−	22.3431i		−	1.17433i
$363$	−18.3808	−	14.2033i	−0.964744	−	0.745482i
$364$	31.8856	+	31.8856i	1.67126	+	1.67126i
$365$	−0.0681918			−0.00356932
$366$	35.9127	+	17.3086i	1.87719	+	0.904735i
$367$	−11.2772			−0.588663			−0.294331	−	0.955703i	$-0.595097\pi$
$367$	−11.2772			−0.588663			−0.294331	+	0.955703i	$0.595097\pi$
$368$	−3.84156	+	3.84156i	−0.200255	+	0.200255i
$369$	0.965361			0.0502547
$370$	−0.155877			−0.00810366
$371$	12.2564			0.636318
$372$	−31.9785	−	31.9785i	−1.65801	−	1.65801i
$373$	7.26985	+	7.26985i	0.376419	+	0.376419i	0.869808	−	0.493390i	$-0.164242\pi$
$373$	7.26985	+	7.26985i	0.376419	+	0.376419i	−0.493390	+	0.869808i	$0.664242\pi$
$374$	11.2453	+	22.9009i	0.581480	+	1.18418i
$375$	0.192395			0.00993524
$376$	18.7001	−	18.7001i	0.964382	−	0.964382i
$377$	8.41413	+	8.41413i	0.433350	+	0.433350i
$378$	17.2120			0.885290
$379$	29.4542			1.51296			0.756480	−	0.654017i	$-0.226918\pi$
$379$	29.4542			1.51296			0.756480	+	0.654017i	$0.226918\pi$
$380$	0.0808046			0.00414519
$381$			25.3250i			1.29744i
$382$			20.4655i			1.04710i
$383$	6.45565	+	6.45565i	0.329868	+	0.329868i	0.852536	−	0.522668i	$-0.175063\pi$
$383$	6.45565	+	6.45565i	0.329868	+	0.329868i	−0.522668	+	0.852536i	$0.675063\pi$
$384$	30.6251	+	30.6251i	1.56283	+	1.56283i
$385$	−0.0625938	−	0.0213661i	−0.00319008	−	0.00108892i
$386$	−23.9099			−1.21698
$387$	8.68484	−	8.68484i	0.441475	−	0.441475i
$388$	16.0063			0.812598
$389$	12.3456	−	12.3456i	0.625946	−	0.625946i	−0.321099	−	0.947046i	$-0.604052\pi$
$389$	12.3456	−	12.3456i	0.625946	−	0.625946i	0.947046	+	0.321099i	$0.104052\pi$
$390$	−0.176306	+	0.176306i	−0.00892761	+	0.00892761i
$391$		−	5.61365i		−	0.283895i
$392$	−6.95679	−	6.95679i	−0.351371	−	0.351371i
$393$	−45.0533			−2.27264
$394$	5.26400	+	5.26400i	0.265197	+	0.265197i
$395$	−0.00492896	+	0.00492896i	−0.000248003	+	0.000248003i
$396$	−16.6951	+	8.19795i	−0.838958	+	0.411962i
$397$	3.29385	+	3.29385i	0.165313	+	0.165313i	0.784916	−	0.619602i	$-0.212706\pi$
$397$	3.29385	+	3.29385i	0.165313	+	0.165313i	−0.619602	+	0.784916i	$0.712706\pi$
$398$	12.4982	+	12.4982i	0.626479	+	0.626479i
$399$	−7.54389	+	7.54389i	−0.377667	+	0.377667i
$400$	−15.3994			−0.769968
$401$	−22.3912	−	22.3912i	−1.11816	−	1.11816i	−0.992011	−	0.126154i	$-0.959737\pi$
$401$	−22.3912	−	22.3912i	−1.11816	−	1.11816i	−0.126154	−	0.992011i	$-0.540263\pi$
$402$	4.52143			0.225508
$403$	21.1294	−	21.1294i	1.05253	−	1.05253i
$404$	10.2452	−	10.2452i	0.509718	−	0.509718i
$405$			0.102482i			0.00509237i
$406$	8.30299	+	8.30299i	0.412070	+	0.412070i
$407$	7.58370	−	22.2171i	0.375910	−	1.10126i
$408$	29.9306			1.48179
$409$	−18.3343	+	18.3343i	−0.906571	+	0.906571i	−0.995994	−	0.0894226i	$-0.971498\pi$
$409$	−18.3343	+	18.3343i	−0.906571	+	0.906571i	0.0894226	+	0.995994i	$0.471498\pi$
$410$	0.0103003	−	0.0103003i	0.000508697	−	0.000508697i
$411$			43.1762i			2.12972i
$412$		−	33.9286i		−	1.67154i
$413$			21.2389i			1.04510i
$414$	6.22250			0.305819
$415$	0.0436295			0.00214169
$416$	−5.54510	+	5.54510i	−0.271871	+	0.271871i
$417$	−15.2481	−	15.2481i	−0.746705	−	0.746705i
$418$	−5.97749	+	17.5116i	−0.292369	+	0.856519i
$419$	−7.93006	+	7.93006i	−0.387409	+	0.387409i	−0.873762	−	0.486353i	$-0.838327\pi$
$419$	−7.93006	+	7.93006i	−0.387409	+	0.387409i	0.486353	+	0.873762i	$0.338327\pi$
$420$	−0.114422	+	0.114422i	−0.00558321	+	0.00558321i
$421$	−10.9099	+	10.9099i	−0.531717	+	0.531717i	−0.921083	−	0.389366i	$-0.872694\pi$
$421$	−10.9099	+	10.9099i	−0.531717	+	0.531717i	0.389366	+	0.921083i	$0.372694\pi$
$422$	−27.2209			−1.32509
$423$	−8.66618			−0.421364
$424$		−	24.9382i		−	1.21110i
$425$	11.2515	−	11.2515i	0.545779	−	0.545779i
$426$	−69.7825			−3.38097
$427$	−7.42218	+	15.3999i	−0.359184	+	0.745254i
$428$			70.0515i			3.38607i
$429$	−16.5512	−	33.7065i	−0.799102	−	1.62736i
$430$		−	0.185333i		−	0.00893755i
$431$	22.4060			1.07926			0.539629	−	0.841903i	$-0.318565\pi$
$431$	22.4060			1.07926			0.539629	+	0.841903i	$0.318565\pi$
$432$		−	10.0199i		−	0.482081i
$433$	16.2656	+	16.2656i	0.781675	+	0.781675i	0.980113	−	0.198438i	$-0.0635870\pi$
$433$	16.2656	+	16.2656i	0.781675	+	0.781675i	−0.198438	+	0.980113i	$0.563587\pi$
$434$	20.8503	−	20.8503i	1.00085	−	1.00085i
$435$	−0.0301941	+	0.0301941i	−0.00144770	+	0.00144770i
$436$			44.3772i			2.12528i
$437$	2.87891	−	2.87891i	0.137717	−	0.137717i
$438$	−27.0146	−	27.0146i	−1.29081	−	1.29081i
$439$		−	39.4379i		−	1.88227i	−0.338036	−	0.941133i	$-0.609763\pi$
$439$		−	39.4379i		−	1.88227i	0.338036	−	0.941133i	$-0.390237\pi$
$440$	−0.0434739	+	0.127360i	−0.00207253	+	0.00607167i
$441$			3.22399i			0.153523i
$442$			41.2428i			1.96172i
$443$	−20.2779			−0.963432			−0.481716	−	0.876327i	$-0.659986\pi$
$443$	−20.2779			−0.963432			−0.481716	+	0.876327i	$0.659986\pi$
$444$	−40.6129	−	40.6129i	−1.92740	−	1.92740i
$445$	−0.0514292	+	0.0514292i	−0.00243798	+	0.00243798i
$446$	−62.3159			−2.95074
$447$		−	25.7902i		−	1.21983i
$448$	−15.0056	+	15.0056i	−0.708949	+	0.708949i
$449$	−40.8382			−1.92728			−0.963638	−	0.267211i	$-0.913898\pi$
$449$	−40.8382			−1.92728			−0.963638	+	0.267211i	$0.913898\pi$
$450$	12.4718	+	12.4718i	0.587928	+	0.587928i
$451$	0.966973	+	1.96923i	0.0455330	+	0.0927275i
$452$	4.24420			0.199630
$453$	−6.40365	−	6.40365i	−0.300870	−	0.300870i
$454$			22.7954i			1.06984i
$455$	−0.0756027	−	0.0756027i	−0.00354431	−	0.00354431i
$456$	15.3496	+	15.3496i	0.718813	+	0.718813i
$457$	−2.42390	−	2.42390i	−0.113385	−	0.113385i	0.648138	−	0.761523i	$-0.275548\pi$
$457$	−2.42390	−	2.42390i	−0.113385	−	0.113385i	−0.761523	+	0.648138i	$0.775548\pi$
$458$	37.7958	−	37.7958i	1.76608	−	1.76608i
$459$	7.32100	+	7.32100i	0.341715	+	0.341715i
$460$	0.0436658	−	0.0436658i	0.00203593	−	0.00203593i
$461$			16.9589i			0.789853i	0.918713	+	0.394926i	$0.129230\pi$
$461$			16.9589i			0.789853i	−0.918713	+	0.394926i	$0.870770\pi$
$462$	−16.3326	−	33.2612i	−0.759862	−	1.54745i
$463$		−	16.2011i		−	0.752929i	−0.926431	−	0.376464i	$-0.877140\pi$
$463$		−	16.2011i		−	0.752929i	0.926431	−	0.376464i	$-0.122860\pi$
$464$	4.83354	−	4.83354i	0.224391	−	0.224391i
$465$	0.0758228	+	0.0758228i	0.00351620	+	0.00351620i
$466$			54.9016i			2.54327i
$467$	−14.0114	+	14.0114i	−0.648370	+	0.648370i	−0.952599	−	0.304229i	$-0.901601\pi$
$467$	−14.0114	+	14.0114i	−0.648370	+	0.648370i	0.304229	+	0.952599i	$0.401601\pi$
$468$	−30.0665			−1.38983
$469$			1.93886i			0.0895280i
$470$	−0.0924674	+	0.0924674i	−0.00426520	+	0.00426520i
$471$	5.23063	−	5.23063i	0.241015	−	0.241015i
$472$	43.2151			1.98914
$473$	26.4155	+	9.01679i	1.21458	+	0.414592i
$474$	−3.90527			−0.179375
$475$	11.5405			0.529514
$476$			26.7664i			1.22683i
$477$	−5.77855	+	5.77855i	−0.264582	+	0.264582i
$478$	31.4735	−	31.4735i	1.43956	−	1.43956i
$479$	16.1628			0.738496			0.369248	−	0.929331i	$-0.379615\pi$
$479$	16.1628			0.738496			0.369248	+	0.929331i	$0.379615\pi$
$480$	−0.0198986	−	0.0198986i	−0.000908242	−	0.000908242i
$481$	26.8345	−	26.8345i	1.22355	−	1.22355i
$482$	−12.4822	+	12.4822i	−0.568547	+	0.568547i
$483$			8.15326i			0.370986i
$484$	−33.4458	−	25.8445i	−1.52027	−	1.17475i
$485$	−0.0379519			−0.00172331
$486$	−23.9176	+	23.9176i	−1.08492	+	1.08492i
$487$		−	43.2860i		−	1.96147i	−0.195333	−	0.980737i	$-0.562579\pi$
$487$		−	43.2860i		−	1.96147i	0.195333	−	0.980737i	$-0.437421\pi$
$488$	31.3344	+	15.1020i	1.41844	+	0.683636i
$489$	35.4069			1.60115
$490$	0.0343997	+	0.0343997i	0.00155402	+	0.00155402i
$491$	−2.21035			−0.0997517			−0.0498759	−	0.998755i	$-0.515883\pi$
$491$	−2.21035			−0.0997517			−0.0498759	+	0.998755i	$0.515883\pi$
$492$	5.36739			0.241981
$493$			7.06323i			0.318112i
$494$	−21.1510	+	21.1510i	−0.951629	+	0.951629i
$495$	0.0395849	−	0.0194378i	0.00177921	−	0.000873664i
$496$	−12.1379	−	12.1379i	−0.545006	−	0.545006i
$497$		−	29.9238i		−	1.34226i
$498$	17.2841	+	17.2841i	0.774518	+	0.774518i
$499$	18.8152	+	18.8152i	0.842284	+	0.842284i	0.989156	−	0.146871i	$-0.0469203\pi$
$499$	18.8152	+	18.8152i	0.842284	+	0.842284i	−0.146871	+	0.989156i	$0.546920\pi$
$500$	0.350083			0.0156562
$501$			9.94789i			0.444439i
$502$	−5.38570			−0.240376
$503$			13.6489i			0.608575i	0.952580	+	0.304287i	$0.0984183\pi$
$503$			13.6489i			0.608575i	−0.952580	+	0.304287i	$0.901582\pi$
$504$	−14.2267			−0.633708
$505$	−0.0242920	+	0.0242920i	−0.00108098	+	0.00108098i
$506$	6.23288	+	12.6932i	0.277085	+	0.564282i
$507$		−	33.2502i		−	1.47669i
$508$			46.0815i			2.04454i
$509$	2.03895	+	2.03895i	0.0903749	+	0.0903749i	0.750849	−	0.660474i	$-0.229645\pi$
$509$	2.03895	+	2.03895i	0.0903749	+	0.0903749i	−0.660474	+	0.750849i	$0.729645\pi$
$510$	−0.148000			−0.00655355
$511$	11.5843	−	11.5843i	0.512458	−	0.512458i
$512$	22.5839	+	22.5839i	0.998076	+	0.998076i
$513$			7.50902i			0.331531i
$514$	18.3675	+	18.3675i	0.810156	+	0.810156i
$515$			0.0804467i			0.00354491i
$516$	48.2876	−	48.2876i	2.12574	−	2.12574i
$517$	−8.68065	−	17.6781i	−0.381774	−	0.777480i
$518$	26.4800	−	26.4800i	1.16346	−	1.16346i
$519$	12.1752	−	12.1752i	0.534432	−	0.534432i
$520$	−0.153830	+	0.153830i	−0.00674588	+	0.00674588i
$521$	−29.2523	+	29.2523i	−1.28157	+	1.28157i	−0.341793	+	0.939775i	$0.611034\pi$
$521$	−29.2523	+	29.2523i	−1.28157	+	1.28157i	−0.939775	+	0.341793i	$0.888966\pi$
$522$	−7.82929			−0.342679
$523$	27.4267	−	27.4267i	1.19929	−	1.19929i	0.224906	−	0.974380i	$-0.427793\pi$
$523$	27.4267	−	27.4267i	1.19929	−	1.19929i	0.974380	−	0.224906i	$-0.0722075\pi$
$524$	−81.9792			−3.58128
$525$	−16.3417	+	16.3417i	−0.713210	+	0.713210i
$526$	−19.5548	−	19.5548i	−0.852630	−	0.852630i
$527$	17.7370			0.772637
$528$	−19.3628	+	9.50794i	−0.842659	+	0.413780i
$529$			19.8885i			0.864719i
$530$			0.123313i			0.00535639i
$531$	−10.0136	−	10.0136i	−0.434553	−	0.434553i
$532$	−13.7269	+	13.7269i	−0.595136	+	0.595136i
$533$			3.54644i			0.153613i
$534$	−40.7480			−1.76334
$535$		−	0.166096i		−	0.00718096i
$536$	3.94501			0.170399
$537$			31.0318i			1.33912i
$538$	9.17609	+	9.17609i	0.395609	+	0.395609i
$539$	−6.57659	+	3.22937i	−0.283274	+	0.139099i
$540$			0.113893i			0.00490117i
$541$	6.87423	+	6.87423i	0.295546	+	0.295546i	0.839266	−	0.543720i	$-0.182985\pi$
$541$	6.87423	+	6.87423i	0.295546	+	0.295546i	−0.543720	+	0.839266i	$0.682985\pi$
$542$	−28.6150	−	28.6150i	−1.22912	−	1.22912i
$543$	−13.8028	+	13.8028i	−0.592335	+	0.592335i
$544$	−4.65482			−0.199574
$545$		−	0.105221i		−	0.00450717i
$546$		−	59.9009i		−	2.56352i
$547$	−17.0151	+	17.0151i	−0.727514	+	0.727514i	−0.970124	−	0.242610i	$-0.921997\pi$
$547$	−17.0151	+	17.0151i	−0.727514	+	0.727514i	0.242610	+	0.970124i	$0.421997\pi$
$548$			78.5635i			3.35607i
$549$	−3.76130	−	10.7600i	−0.160528	−	0.459227i
$550$	−12.9485	+	37.9338i	−0.552127	+	1.61750i
$551$	−3.62232	+	3.62232i	−0.154316	+	0.154316i
$552$	16.5895			0.706097
$553$		−	1.67464i		−	0.0712129i
$554$			44.3932i			1.88609i
$555$	0.0962956	+	0.0962956i	0.00408752	+	0.00408752i
$556$	−27.7456	−	27.7456i	−1.17667	−	1.17667i
$557$	−29.7856	+	29.7856i	−1.26206	+	1.26206i	−0.311961	+	0.950095i	$0.600986\pi$
$557$	−29.7856	+	29.7856i	−1.26206	+	1.26206i	−0.950095	+	0.311961i	$0.899014\pi$
$558$			19.6607i			0.832305i
$559$	31.9054	+	31.9054i	1.34945	+	1.34945i
$560$	−0.0434303	+	0.0434303i	−0.00183526	+	0.00183526i
$561$	7.20046	−	21.0944i	0.304004	−	0.890606i
$562$	14.4187			0.608218
$563$	2.35357			0.0991912			0.0495956	−	0.998769i	$-0.484207\pi$
$563$	2.35357			0.0991912			0.0495956	+	0.998769i	$0.484207\pi$
$564$	−48.1838			−2.02890
$565$	−0.0100632			−0.000423364
$566$	52.0657	+	52.0657i	2.18848	+	2.18848i
$567$	−17.4094	−	17.4094i	−0.731125	−	0.731125i
$568$	−60.8863			−2.55473
$569$		−	19.8765i		−	0.833268i	−0.909074	−	0.416634i	$-0.863210\pi$
$569$		−	19.8765i		−	0.833268i	0.909074	−	0.416634i	$-0.136790\pi$
$570$	−0.0759004	−	0.0759004i	−0.00317912	−	0.00317912i
$571$			5.98429i			0.250435i	0.992129	+	0.125217i	$0.0399629\pi$
$571$			5.98429i			0.250435i	−0.992129	+	0.125217i	$0.960037\pi$
$572$	−30.1167	−	61.3324i	−1.25924	−	2.56444i
$573$	12.6429	−	12.6429i	0.528164	−	0.528164i
$574$			3.49959i			0.146070i
$575$	6.23634	−	6.23634i	0.260073	−	0.260073i
$576$		−	14.1495i		−	0.589563i
$577$	26.9320	+	26.9320i	1.12119	+	1.12119i	0.991562	+	0.129631i	$0.0413794\pi$
$577$	26.9320	+	26.9320i	1.12119	+	1.12119i	0.129631	+	0.991562i	$0.458621\pi$
$578$	11.7453	−	11.7453i	0.488539	−	0.488539i
$579$	14.7708	+	14.7708i	0.613852	+	0.613852i
$580$	−0.0549413	+	0.0549413i	−0.00228132	+	0.00228132i
$581$	−7.41167	+	7.41167i	−0.307488	+	0.307488i
$582$	−15.0349	−	15.0349i	−0.623216	−	0.623216i
$583$	−17.5758	−	5.99942i	−0.727916	−	0.248471i
$584$	−23.5707	−	23.5707i	−0.975361	−	0.975361i
$585$	0.0712894			0.00294745
$586$	4.62356	+	4.62356i	0.190998	+	0.190998i
$587$	25.3785	+	25.3785i	1.04748	+	1.04748i	0.998815	+	0.0486666i	$0.0154972\pi$
$587$	25.3785	+	25.3785i	1.04748	+	1.04748i	0.0486666	+	0.998815i	$0.484503\pi$
$588$			17.9253i			0.739228i
$589$	9.09627	+	9.09627i	0.374805	+	0.374805i
$590$	−0.213689			−0.00879742
$591$		−	6.50385i		−	0.267533i
$592$	−15.4152	−	15.4152i	−0.633560	−	0.633560i
$593$	13.0768	+	13.0768i	0.536999	+	0.536999i	0.922646	−	0.385647i	$-0.126022\pi$
$593$	13.0768	+	13.0768i	0.536999	+	0.536999i	−0.385647	+	0.922646i	$0.626022\pi$
$594$	−24.6823	−	8.42518i	−1.01273	−	0.345690i
$595$		−	0.0634646i		−	0.00260179i
$596$		−	46.9279i		−	1.92224i
$597$		−	15.4419i		−	0.631997i
$598$			22.8595i			0.934794i
$599$	7.49897	−	7.49897i	0.306400	−	0.306400i	−0.537112	−	0.843511i	$-0.680485\pi$
$599$	7.49897	−	7.49897i	0.306400	−	0.306400i	0.843511	+	0.537112i	$0.180485\pi$
$600$	33.2506	+	33.2506i	1.35745	+	1.35745i
$601$	−8.54963			−0.348747			−0.174373	−	0.984680i	$-0.555790\pi$
$601$	−8.54963			−0.348747			−0.174373	+	0.984680i	$0.555790\pi$
$602$	31.4839	+	31.4839i	1.28319	+	1.28319i
$603$	−0.914120	−	0.914120i	−0.0372258	−	0.0372258i
$604$	−11.6521	−	11.6521i	−0.474118	−	0.474118i
$605$	0.0793020	+	0.0612787i	0.00322409	+	0.00249133i
$606$	−19.2468			−0.781849
$607$			25.9521i			1.05336i	0.850063	+	0.526682i	$0.176564\pi$
$607$			25.9521i			1.05336i	−0.850063	+	0.526682i	$0.823436\pi$
$608$	−2.38718	−	2.38718i	−0.0968131	−	0.0968131i
$609$		−	10.2586i		−	0.415700i
$610$	−0.154941	−	0.0746759i	−0.00627339	−	0.00302354i
$611$		−	31.8368i		−	1.28798i
$612$	−12.6196	−	12.6196i	−0.510119	−	0.510119i
$613$	8.57431			0.346313			0.173157	−	0.984894i	$-0.444603\pi$
$613$	8.57431			0.346313			0.173157	+	0.984894i	$0.444603\pi$
$614$			73.0658i			2.94870i
$615$	−0.0127264			−0.000513178
$616$	−14.2505	−	29.0209i	−0.574167	−	1.16929i
$617$	21.9479	−	21.9479i	0.883590	−	0.883590i	−0.110308	−	0.993897i	$-0.535184\pi$
$617$	21.9479	−	21.9479i	0.883590	−	0.883590i	0.993897	+	0.110308i	$0.0351837\pi$
$618$	−31.8695	+	31.8695i	−1.28198	+	1.28198i
$619$	9.45491			0.380025			0.190012	−	0.981782i	$-0.439147\pi$
$619$	9.45491			0.380025			0.190012	+	0.981782i	$0.439147\pi$
$620$	0.137967	+	0.137967i	0.00554090	+	0.00554090i
$621$	4.05778	+	4.05778i	0.162833	+	0.162833i
$622$			23.3292i			0.935414i
$623$		−	17.4733i		−	0.700055i
$624$	−34.8710			−1.39596
$625$	24.9988			0.999950
$626$			57.6115i			2.30262i
$627$	14.5108	−	7.12537i	0.579504	−	0.284560i
$628$	9.51767	−	9.51767i	0.379796	−	0.379796i
$629$	22.5262			0.898177
$630$	0.0703477			0.00280272
$631$	−2.70479	−	2.70479i	−0.107676	−	0.107676i	0.651216	−	0.758892i	$-0.274259\pi$
$631$	−2.70479	−	2.70479i	−0.107676	−	0.107676i	−0.758892	+	0.651216i	$0.774259\pi$
$632$	−3.40741			−0.135540
$633$	16.8162	+	16.8162i	0.668383	+	0.668383i
$634$	−13.8480	−	13.8480i	−0.549974	−	0.549974i
$635$		−	0.109262i		−	0.00433593i
$636$	−32.1287	+	32.1287i	−1.27398	+	1.27398i
$637$	−11.8439			−0.469274
$638$	−7.84236	−	15.9709i	−0.310482	−	0.632294i
$639$	14.1083	+	14.1083i	0.558115	+	0.558115i
$640$	−0.132128	−	0.132128i	−0.00522284	−	0.00522284i
$641$	−28.4925	−	28.4925i	−1.12539	−	1.12539i	−0.990918	−	0.134469i	$-0.957067\pi$
$641$	−28.4925	−	28.4925i	−1.12539	−	1.12539i	−0.134469	−	0.990918i	$-0.542933\pi$
$642$	65.8000	−	65.8000i	2.59692	−	2.59692i
$643$	13.7333	−	13.7333i	0.541587	−	0.541587i	−0.382407	−	0.923994i	$-0.624905\pi$
$643$	13.7333	−	13.7333i	0.541587	−	0.541587i	0.923994	+	0.382407i	$0.124905\pi$
$644$			14.8357i			0.584608i
$645$	−0.114493	+	0.114493i	−0.00450814	+	0.00450814i
$646$	−17.7552			−0.698568
$647$	−26.5276	−	26.5276i	−1.04291	−	1.04291i	−0.999037	−	0.0438695i	$-0.986031\pi$
$647$	−26.5276	−	26.5276i	−1.04291	−	1.04291i	−0.0438695	−	0.999037i	$-0.513969\pi$
$648$	−35.4231	+	35.4231i	−1.39155	+	1.39155i
$649$	10.3963	−	30.4570i	0.408092	−	1.19554i
$650$	−45.8176	+	45.8176i	−1.79711	+	1.79711i
$651$	−25.7612			−1.00966
$652$	64.4264			2.52313
$653$	21.9239	+	21.9239i	0.857950	+	0.857950i	0.991096	−	0.133147i	$-0.0425081\pi$
$653$	21.9239	+	21.9239i	0.857950	+	0.857950i	−0.133147	+	0.991096i	$0.542508\pi$
$654$	41.6839	−	41.6839i	1.62997	−	1.62997i
$655$	0.194377			0.00759495
$656$	2.03727			0.0795418
$657$			10.9234i			0.426161i
$658$		−	31.4163i		−	1.22473i
$659$	−48.7844			−1.90037			−0.950186	−	0.311684i	$-0.899107\pi$
$659$	−48.7844			−1.90037			−0.950186	+	0.311684i	$0.899107\pi$
$660$	0.220091	−	0.108074i	0.00856705	−	0.00420677i
$661$	15.0246	−	15.0246i	0.584391	−	0.584391i	−0.351716	−	0.936107i	$-0.614402\pi$
$661$	15.0246	−	15.0246i	0.584391	−	0.584391i	0.936107	+	0.351716i	$0.114402\pi$
$662$	59.2802			2.30399
$663$	25.4784	−	25.4784i	0.989500	−	0.989500i
$664$	15.0806	+	15.0806i	0.585241	+	0.585241i
$665$	0.0325472	−	0.0325472i	0.00126213	−	0.00126213i
$666$			24.9693i			0.967540i
$667$			3.91491i			0.151586i
$668$			18.1012i			0.700357i
$669$	38.4967	+	38.4967i	1.48837	+	1.48837i
$670$	−0.0195072			−0.000753628
$671$	18.1817	−	18.4506i	0.701897	−	0.712278i
$672$	6.76065			0.260798
$673$	−15.3764	−	15.3764i	−0.592716	−	0.592716i	0.345648	−	0.938364i	$-0.387659\pi$
$673$	−15.3764	−	15.3764i	−0.592716	−	0.592716i	−0.938364	+	0.345648i	$0.887659\pi$
$674$		−	3.94597i		−	0.151993i
$675$			16.2661i			0.626084i
$676$		−	60.5022i		−	2.32701i
$677$	6.00709	−	6.00709i	0.230871	−	0.230871i	−0.582185	−	0.813056i	$-0.697802\pi$
$677$	6.00709	−	6.00709i	0.230871	−	0.230871i	0.813056	+	0.582185i	$0.197802\pi$
$678$	−3.98662	−	3.98662i	−0.153105	−	0.153105i
$679$	6.44718	−	6.44718i	0.247420	−	0.247420i
$680$	−0.129132			−0.00495199
$681$	14.0822	−	14.0822i	0.539632	−	0.539632i
$682$	−40.1057	+	19.6935i	−1.53573	+	0.754105i
$683$	−33.1932			−1.27010			−0.635052	−	0.772470i	$-0.719021\pi$
$683$	−33.1932			−1.27010			−0.635052	+	0.772470i	$0.719021\pi$
$684$		−	12.9437i		−	0.494916i
$685$		−	0.186279i		−	0.00711734i
$686$	−48.7221			−1.86022
$687$	−46.6980			−1.78164
$688$	18.3282	−	18.3282i	0.698756	−	0.698756i
$689$	−21.2286	−	21.2286i	−0.808745	−	0.808745i
$690$	−0.0820314			−0.00312288
$691$	−12.5183			−0.476218			−0.238109	−	0.971238i	$-0.576528\pi$
$691$	−12.5183			−0.476218			−0.238109	+	0.971238i	$0.576528\pi$
$692$	22.1540	−	22.1540i	0.842170	−	0.842170i
$693$	−3.42255	+	10.0266i	−0.130012	+	0.380881i
$694$	46.7225	−	46.7225i	1.77356	−	1.77356i
$695$	0.0657863	+	0.0657863i	0.00249542	+	0.00249542i
$696$	−20.8733			−0.791202
$697$	−1.48852	+	1.48852i	−0.0563819	+	0.0563819i
$698$			11.6467i			0.440833i
$699$	33.9164	−	33.9164i	1.28284	−	1.28284i
$700$	−29.7354	+	29.7354i	−1.12389	+	1.12389i
$701$	−24.6727	−	24.6727i	−0.931876	−	0.931876i	0.0659471	−	0.997823i	$-0.478993\pi$
$701$	−24.6727	−	24.6727i	−0.931876	−	0.931876i	−0.997823	+	0.0659471i	$0.978993\pi$
$702$	−29.8120	−	29.8120i	−1.12518	−	1.12518i
$703$	11.5523	+	11.5523i	0.435705	+	0.435705i
$704$	28.8635	−	14.1731i	1.08783	−	0.534170i
$705$	0.114247			0.00430277
$706$	−10.2860	+	10.2860i	−0.387120	+	0.387120i
$707$		−	8.25332i		−	0.310398i
$708$	−55.6754	−	55.6754i	−2.09241	−	2.09241i
$709$	−5.76144	−	5.76144i	−0.216376	−	0.216376i	0.590594	−	0.806969i	$-0.298894\pi$
$709$	−5.76144	−	5.76144i	−0.216376	−	0.216376i	−0.806969	+	0.590594i	$0.798894\pi$
$710$	0.301068			0.0112989
$711$	0.789549	+	0.789549i	0.0296104	+	0.0296104i
$712$	−35.5532			−1.33241
$713$	9.83103			0.368175
$714$	25.1419	−	25.1419i	0.940911	−	0.940911i
$715$	0.0714084	+	0.145423i	0.00267052	+	0.00543850i
$716$			56.4656i			2.11022i
$717$	−38.8866			−1.45225
$718$	38.2592			1.42782
$719$		−	5.11594i		−	0.190792i	−0.995439	−	0.0953961i	$-0.969588\pi$
$719$		−	5.11594i		−	0.190792i	0.995439	−	0.0953961i	$-0.0304118\pi$
$720$		−	0.0409525i		−	0.00152621i
$721$	−13.6661	−	13.6661i	−0.508952	−	0.508952i
$722$	23.3686	+	23.3686i	0.869690	+	0.869690i
$723$	15.4221			0.573555
$724$	−25.1156	+	25.1156i	−0.933415	+	0.933415i
$725$	−7.84671	+	7.84671i	−0.291420	+	0.291420i
$726$	7.14005	+	55.6919i	0.264992	+	2.06692i
$727$	23.6766			0.878117			0.439058	−	0.898459i	$-0.355312\pi$
$727$	23.6766			0.878117			0.439058	+	0.898459i	$0.355312\pi$
$728$		−	52.2645i		−	1.93705i
$729$	−4.19407			−0.155336
$730$	0.116551	+	0.116551i	0.00431376	+	0.00431376i
$731$			26.7829i			0.990602i
$732$	−20.9127	−	59.8256i	−0.772957	−	2.21122i
$733$			34.6531i			1.27994i	0.768400	+	0.639970i	$0.221053\pi$
$733$			34.6531i			1.27994i	−0.768400	+	0.639970i	$0.778947\pi$
$734$	19.2746	+	19.2746i	0.711437	+	0.711437i
$735$		−	0.0425020i		−	0.00156771i
$736$	−2.58001			−0.0951005
$737$	0.949059	−	2.78035i	0.0349590	−	0.102416i
$738$	−1.64997	−	1.64997i	−0.0607361	−	0.0607361i
$739$	−18.4564	−	18.4564i	−0.678930	−	0.678930i	0.280828	−	0.959758i	$-0.409391\pi$
$739$	−18.4564	−	18.4564i	−0.678930	−	0.678930i	−0.959758	+	0.280828i	$0.909391\pi$
$740$	0.175220	+	0.175220i	0.00644120	+	0.00644120i
$741$	26.1328			0.960011
$742$	−20.9482	−	20.9482i	−0.769032	−	0.769032i
$743$	−37.0483	+	37.0483i	−1.35917	+	1.35917i	−0.484231	+	0.874940i	$0.660901\pi$
$743$	−37.0483	+	37.0483i	−1.35917	+	1.35917i	−0.874940	+	0.484231i	$0.839099\pi$
$744$			52.4166i			1.92169i
$745$			0.111269i			0.00407657i
$746$		−	24.8508i		−	0.909853i
$747$		−	6.98882i		−	0.255708i
$748$	13.1020	−	38.3834i	0.479056	−	1.40344i
$749$	28.2160	+	28.2160i	1.03099	+	1.03099i
$750$	−0.328836	−	0.328836i	−0.0120074	−	0.0120074i
$751$		−	23.1381i		−	0.844322i	−0.906521	−	0.422161i	$-0.861272\pi$
$751$		−	23.1381i		−	0.844322i	0.906521	−	0.422161i	$-0.138728\pi$
$752$	−18.2888			−0.666924
$753$	3.32711	+	3.32711i	0.121246	+	0.121246i
$754$		−	28.7624i		−	1.04746i
$755$	0.0276278	+	0.0276278i	0.00100548	+	0.00100548i
$756$	−19.3478	−	19.3478i	−0.703674	−	0.703674i
$757$	−28.9295			−1.05146			−0.525730	−	0.850651i	$-0.676208\pi$
$757$	−28.9295			−1.05146			−0.525730	+	0.850651i	$0.676208\pi$
$758$	−50.3422	−	50.3422i	−1.82851	−	1.82851i
$759$	3.99098	−	11.6919i	0.144863	−	0.424389i
$760$	−0.0662243	−	0.0662243i	−0.00240221	−	0.00240221i
$761$	−17.4245	+	17.4245i	−0.631639	+	0.631639i	−0.948479	−	0.316840i	$-0.897378\pi$
$761$	−17.4245	+	17.4245i	−0.631639	+	0.631639i	0.316840	+	0.948479i	$0.397378\pi$
$762$	43.2848	−	43.2848i	1.56804	−	1.56804i
$763$	17.8747	+	17.8747i	0.647107	+	0.647107i
$764$	23.0050	−	23.0050i	0.832293	−	0.832293i
$765$	0.0299219	+	0.0299219i	0.00108183	+	0.00108183i
$766$		−	22.0676i		−	0.797334i
$767$	36.7868	−	36.7868i	1.32830	−	1.32830i
$768$		−	63.7394i		−	2.30000i
$769$	10.4008	−	10.4008i	0.375063	−	0.375063i	−0.494254	−	0.869317i	$-0.664559\pi$
$769$	10.4008	−	10.4008i	0.375063	−	0.375063i	0.869317	+	0.494254i	$0.164559\pi$
$770$	0.0704652	+	0.143502i	0.00253939	+	0.00517144i
$771$		−	22.6937i		−	0.817292i
$772$	26.8769	+	26.8769i	0.967321	+	0.967321i
$773$			7.44145i			0.267650i	0.991005	+	0.133825i	$0.0427261\pi$
$773$			7.44145i			0.267650i	−0.991005	+	0.133825i	$0.957274\pi$
$774$	−29.6877			−1.06710
$775$	19.7045	+	19.7045i	0.707806	+	0.707806i
$776$	−13.1182	−	13.1182i	−0.470914	−	0.470914i
$777$	−32.7169			−1.17371
$778$	−42.2014			−1.51299
$779$	−1.52675			−0.0547016
$780$	0.396368			0.0141922
$781$	−14.6475	+	42.9112i	−0.524130	+	1.53548i
$782$	−9.59469	+	9.59469i	−0.343105	+	0.343105i
$783$	−5.10560	−	5.10560i	−0.182459	−	0.182459i
$784$			6.80380i			0.242993i
$785$	−0.0225669	+	0.0225669i	−0.000805448	+	0.000805448i
$786$	77.0038	+	77.0038i	2.74663	+	2.74663i
$787$	−0.321969	−	0.321969i	−0.0114770	−	0.0114770i	0.701345	−	0.712822i	$-0.252583\pi$
$787$	−0.321969	−	0.321969i	−0.0114770	−	0.0114770i	−0.712822	+	0.701345i	$0.752583\pi$
$788$		−	11.8344i		−	0.421584i
$789$			24.1606i			0.860140i
$790$	0.0168489			0.000599455
$791$	1.70952	−	1.70952i	0.0607835	−	0.0607835i
$792$	20.4013	+	6.96390i	0.724930	+	0.247451i
$793$	39.5290	−	13.8178i	1.40371	−	0.490685i
$794$		−	11.2595i		−	0.399584i
$795$	0.0761789	−	0.0761789i	0.00270179	−	0.00270179i
$796$		−	28.0982i		−	0.995915i
$797$		−	17.3408i		−	0.614242i	−0.951670	−	0.307121i	$-0.900634\pi$
$797$		−	17.3408i		−	0.614242i	0.951670	−	0.307121i	$-0.0993657\pi$
$798$	25.7876			0.912870
$799$	13.3627	−	13.3627i	0.472738	−	0.472738i
$800$	−5.17115	−	5.17115i	−0.182828	−	0.182828i
$801$	8.23823	+	8.23823i	0.291083	+	0.291083i
$802$			76.5408i			2.70275i
$803$	−22.2825	+	10.9416i	−0.786332	+	0.386121i
$804$	−5.08249	−	5.08249i	−0.179246	−	0.179246i
$805$		−	0.0351763i		−	0.00123980i
$806$	−72.2274			−2.54410
$807$		−	11.3374i		−	0.399094i
$808$	−16.7931			−0.590780
$809$			6.40780i			0.225286i	0.993636	+	0.112643i	$0.0359317\pi$
$809$			6.40780i			0.225286i	−0.993636	+	0.112643i	$0.964068\pi$
$810$	0.175159	−	0.175159i	0.00615446	−	0.00615446i
$811$	−38.8347	−	38.8347i	−1.36367	−	1.36367i	−0.869186	−	0.494486i	$-0.835356\pi$
$811$	−38.8347	−	38.8347i	−1.36367	−	1.36367i	−0.494486	−	0.869186i	$-0.664644\pi$
$812$		−	18.6666i		−	0.655070i
$813$			35.3548i			1.23995i
$814$	−50.9346	+	25.0110i	−1.78526	+	0.876634i
$815$	−0.152759			−0.00535090
$816$	−14.6362	−	14.6362i	−0.512369	−	0.512369i
$817$	−13.7354	+	13.7354i	−0.480540	+	0.480540i
$818$	62.6727			2.19130
$819$	−12.1105	+	12.1105i	−0.423174	+	0.423174i
$820$	−0.0231570			−0.000808677
$821$	−21.7202	+	21.7202i	−0.758039	+	0.758039i	−0.975965	−	0.217926i	$-0.930071\pi$
$821$	−21.7202	+	21.7202i	−0.758039	+	0.758039i	0.217926	+	0.975965i	$0.430071\pi$
$822$	73.7954	−	73.7954i	2.57391	−	2.57391i
$823$	−34.6932	+	34.6932i	−1.20933	+	1.20933i	−0.238083	+	0.971245i	$0.576519\pi$
$823$	−34.6932	+	34.6932i	−1.20933	+	1.20933i	−0.971245	+	0.238083i	$0.923481\pi$
$824$	−27.8066	+	27.8066i	−0.968688	+	0.968688i
$825$	31.4334	−	15.4351i	1.09437	−	0.537381i
$826$	36.3009	−	36.3009i	1.26307	−	1.26307i
$827$		−	32.3199i		−	1.12387i	−0.827181	−	0.561936i	$-0.810057\pi$
$827$		−	32.3199i		−	1.12387i	0.827181	−	0.561936i	$-0.189943\pi$
$828$	−6.99465	−	6.99465i	−0.243081	−	0.243081i
$829$		−	28.1300i		−	0.976995i	−0.872565	−	0.488497i	$-0.837545\pi$
$829$		−	28.1300i		−	0.976995i	0.872565	−	0.488497i	$-0.162455\pi$
$830$	−0.0745701	−	0.0745701i	−0.00258837	−	0.00258837i
$831$	27.4247	−	27.4247i	0.951351	−	0.951351i
$832$	51.9809			1.80211
$833$	−4.97119	−	4.97119i	−0.172241	−	0.172241i
$834$			52.1233i			1.80488i
$835$		−	0.0429190i		−	0.00148527i
$836$	26.4038	−	12.9654i	0.913196	−	0.448416i
$837$	−12.8211	+	12.8211i	−0.443161	+	0.443161i
$838$	27.1076			0.936418
$839$			38.5941i			1.33242i	0.745766	+	0.666208i	$0.232084\pi$
$839$			38.5941i			1.33242i	−0.745766	+	0.666208i	$0.767916\pi$
$840$	0.187551			0.00647113
$841$			24.0742i			0.830144i
$842$	37.2938			1.28523
$843$	−8.90741	−	8.90741i	−0.306788	−	0.306788i
$844$	30.5988	+	30.5988i	1.05325	+	1.05325i
$845$			0.143454i			0.00493497i
$846$	14.8120	+	14.8120i	0.509246	+	0.509246i
$847$	−23.8815	+	3.06176i	−0.820579	+	0.105203i
$848$	−12.1949	+	12.1949i	−0.418773	+	0.418773i
$849$		−	64.3289i		−	2.20776i
$850$	−38.4615			−1.31922
$851$	12.4855			0.427997
$852$	78.4418	+	78.4418i	2.68737	+	2.68737i
$853$	13.8880			0.475515			0.237757	−	0.971325i	$-0.423588\pi$
$853$	13.8880			0.475515			0.237757	+	0.971325i	$0.423588\pi$
$854$	39.0068	−	13.6353i	1.33479	−	0.466590i
$855$			0.0306904i			0.00104959i
$856$	57.4115	−	57.4115i	1.96228	−	1.96228i
$857$	11.3429			0.387466			0.193733	−	0.981054i	$-0.437941\pi$
$857$	11.3429			0.387466			0.193733	+	0.981054i	$0.437941\pi$
$858$	−29.3212	+	85.8990i	−1.00101	+	2.93254i
$859$		−	4.44644i		−	0.151710i	−0.997119	−	0.0758552i	$-0.975831\pi$
$859$		−	4.44644i		−	0.151710i	0.997119	−	0.0758552i	$-0.0241687\pi$
$860$	−0.208331	+	0.208331i	−0.00710403	+	0.00710403i
$861$	2.16193	−	2.16193i	0.0736784	−	0.0736784i
$862$	−38.2956	−	38.2956i	−1.30435	−	1.30435i
$863$	8.48645			0.288882			0.144441	−	0.989513i	$-0.453862\pi$
$863$	8.48645			0.288882			0.144441	+	0.989513i	$0.453862\pi$
$864$	3.36470	−	3.36470i	0.114469	−	0.114469i
$865$	−0.0525285	+	0.0525285i	−0.00178602	+	0.00178602i
$866$		−	55.6013i		−	1.88941i
$867$	−14.5117			−0.492842
$868$	−46.8752			−1.59105
$869$	−0.819727	+	2.40146i	−0.0278073	+	0.0814640i
$870$	0.103214			0.00349928
$871$	3.35819	−	3.35819i	0.113788	−	0.113788i
$872$	36.3699	−	36.3699i	1.23164	−	1.23164i
$873$			6.07936i			0.205755i
$874$	−9.84110			−0.332880
$875$	0.141010	−	0.141010i	0.00476700	−	0.00476700i
$876$			60.7337i			2.05200i
$877$	25.6668	+	25.6668i	0.866707	+	0.866707i	0.992106	−	0.125399i	$-0.0400212\pi$
$877$	25.6668	+	25.6668i	0.866707	+	0.866707i	−0.125399	+	0.992106i	$0.540021\pi$
$878$	−67.4060	+	67.4060i	−2.27484	+	2.27484i
$879$		−	5.71256i		−	0.192680i
$880$	0.0835387	−	0.0410209i	0.00281609	−	0.00138281i
$881$		−	20.8007i		−	0.700795i	−0.936601	−	0.350397i	$-0.886047\pi$
$881$		−	20.8007i		−	0.700795i	0.936601	−	0.350397i	$-0.113953\pi$
$882$	5.51035	−	5.51035i	0.185543	−	0.185543i
$883$	−38.8336	−	38.8336i	−1.30685	−	1.30685i	−0.923673	−	0.383181i	$-0.874828\pi$
$883$	−38.8336	−	38.8336i	−1.30685	−	1.30685i	−0.383181	−	0.923673i	$-0.625172\pi$
$884$	46.3606	−	46.3606i	1.55928	−	1.55928i
$885$	0.132010	+	0.132010i	0.00443745	+	0.00443745i
$886$	34.6584	+	34.6584i	1.16437	+	1.16437i
$887$	3.78927	+	3.78927i	0.127231	+	0.127231i	0.767855	−	0.640624i	$-0.221324\pi$
$887$	3.78927	+	3.78927i	0.127231	+	0.127231i	−0.640624	+	0.767855i	$0.721324\pi$
$888$			66.5695i			2.23393i
$889$	18.5611	+	18.5611i	0.622521	+	0.622521i
$890$	0.175802			0.00589291
$891$	16.4436	+	33.4872i	0.550880	+	1.12186i
$892$	70.0487	+	70.0487i	2.34540	+	2.34540i
$893$	13.7059			0.458650
$894$	−44.0798	+	44.0798i	−1.47425	+	1.47425i
$895$		−	0.133883i		−	0.00447522i
$896$	44.8914			1.49971
$897$	14.1218	−	14.1218i	0.471514	−	0.471514i
$898$	69.7995	+	69.7995i	2.32924	+	2.32924i
$899$	−12.3696			−0.412550
$900$		−	28.0389i		−	0.934631i
$901$		−	17.8203i		−	0.593681i
$902$	1.71303	−	5.01847i	0.0570377	−	0.167097i
$903$		−	38.8995i		−	1.29449i
$904$	−3.47838	−	3.47838i	−0.115689	−	0.115689i
$905$	0.0595506	−	0.0595506i	0.00197953	−	0.00197953i
$906$			21.8899i			0.727242i
$907$	−22.1698	+	22.1698i	−0.736137	+	0.736137i	−0.971828	−	0.235691i	$-0.924265\pi$
$907$	−22.1698	+	22.1698i	−0.736137	+	0.736137i	0.235691	+	0.971828i	$0.424265\pi$
$908$	25.6241	−	25.6241i	0.850365	−	0.850365i
$909$	3.89123	+	3.89123i	0.129064	+	0.129064i
$910$			0.258436i			0.00856706i
$911$	−31.7604			−1.05227			−0.526134	−	0.850402i	$-0.676359\pi$
$911$	−31.7604			−1.05227			−0.526134	+	0.850402i	$0.676359\pi$
$912$		−	15.0121i		−	0.497100i
$913$	14.2564	−	7.00049i	0.471819	−	0.231682i
$914$			8.28573i			0.274067i
$915$	0.0495853	+	0.141850i	0.00163924	+	0.00468941i
$916$	−84.9718			−2.80755
$917$	−33.0204	+	33.0204i	−1.09043	+	1.09043i
$918$		−	25.0257i		−	0.825970i
$919$	25.3714			0.836925			0.418463	−	0.908234i	$-0.362569\pi$
$919$	25.3714			0.836925			0.418463	+	0.908234i	$0.362569\pi$
$920$	−0.0715736			−0.00235971
$921$	45.1376	−	45.1376i	1.48733	−	1.48733i
$922$	28.9856	−	28.9856i	0.954589	−	0.954589i
$923$	−51.8294	+	51.8294i	−1.70599	+	1.70599i
$924$	−19.0293	+	55.7480i	−0.626018	+	1.83397i
$925$	25.0248	+	25.0248i	0.822812	+	0.822812i
$926$	−27.6904	+	27.6904i	−0.909963	+	0.909963i
$927$	12.8864			0.423246
$928$	3.24623			0.106563
$929$			17.2530i			0.566051i	0.959112	+	0.283026i	$0.0913381\pi$
$929$			17.2530i			0.566051i	−0.959112	+	0.283026i	$0.908662\pi$
$930$		−	0.259188i		−	0.00849911i
$931$		−	5.09886i		−	0.167108i
$932$	61.7144	−	61.7144i	2.02152	−	2.02152i
$933$	14.4120	−	14.4120i	0.471827	−	0.471827i
$934$	47.8957			1.56720
$935$	−0.0310656	+	0.0910092i	−0.00101595	+	0.00297632i
$936$	24.6413	+	24.6413i	0.805427	+	0.805427i
$937$			2.16397i			0.0706938i	0.999375	+	0.0353469i	$0.0112536\pi$
$937$			2.16397i			0.0706938i	−0.999375	+	0.0353469i	$0.988746\pi$
$938$	3.31383	−	3.31383i	0.108200	−	0.108200i
$939$	35.5905	−	35.5905i	1.16145	−	1.16145i
$940$	0.207883			0.00678041
$941$	27.6380	+	27.6380i	0.900972	+	0.900972i	0.995520	−	0.0945482i	$-0.0301407\pi$
$941$	27.6380	+	27.6380i	0.900972	+	0.900972i	−0.0945482	+	0.995520i	$0.530141\pi$
$942$	−17.8801			−0.582564
$943$	−0.825039	+	0.825039i	−0.0268670	+	0.0268670i
$944$	−21.1324	−	21.1324i	−0.687800	−	0.687800i
$945$	0.0458748	+	0.0458748i	0.00149231	+	0.00149231i
$946$	−29.7373	−	60.5597i	−0.966843	−	1.96897i
$947$	−6.17495	+	6.17495i	−0.200659	+	0.200659i	−0.800282	−	0.599623i	$-0.795317\pi$
$947$	−6.17495	+	6.17495i	−0.200659	+	0.200659i	0.599623	+	0.800282i	$0.295317\pi$
$948$	4.38988	+	4.38988i	0.142577	+	0.142577i
$949$	−40.1290			−1.30264
$950$	−19.7247	−	19.7247i	−0.639952	−	0.639952i
$951$			17.1097i			0.554819i
$952$	21.9367	−	21.9367i	0.710971	−	0.710971i
$953$	−19.9913	+	19.9913i	−0.647582	+	0.647582i	−0.952408	−	0.304826i	$-0.901402\pi$
$953$	−19.9913	+	19.9913i	−0.647582	+	0.647582i	0.304826	+	0.952408i	$0.401402\pi$
$954$	19.7531			0.639529
$955$	−0.0545462	+	0.0545462i	−0.00176507	+	0.00176507i
$956$	−70.7581			−2.28848
$957$	−5.02154	+	14.7110i	−0.162323	+	0.475540i
$958$	−27.6249	−	27.6249i	−0.892520	−	0.892520i
$959$	31.6446	+	31.6446i	1.02186	+	1.02186i
$960$			0.186534i			0.00602035i
$961$			0.0623425i			0.00201105i
$962$	−91.7293			−2.95747
$963$	−26.6062			−0.857374
$964$	28.0622			0.903821
$965$	−0.0637267	−	0.0637267i	−0.00205143	−	0.00205143i
$966$	13.9353	−	13.9353i	0.448361	−	0.448361i
$967$	2.92744			0.0941400			0.0470700	−	0.998892i	$-0.485012\pi$
$967$	2.92744			0.0941400			0.0470700	+	0.998892i	$0.485012\pi$
$968$	6.22980	+	48.5920i	0.200233	+	1.56181i
$969$	10.9686	+	10.9686i	0.352361	+	0.352361i
$970$	0.0648662	+	0.0648662i	0.00208273	+	0.00208273i
$971$	−33.4485			−1.07341			−0.536706	−	0.843769i	$-0.680332\pi$
$971$	−33.4485			−1.07341			−0.536706	+	0.843769i	$0.680332\pi$
$972$	53.7711			1.72471
$973$	−22.3512			−0.716548
$974$	−73.9830	+	73.9830i	−2.37057	+	2.37057i
$975$	56.6092			1.81294
$976$	−7.93771	−	22.7076i	−0.254080	−	0.726852i
$977$	−42.8990			−1.37246			−0.686230	−	0.727385i	$-0.740736\pi$
$977$	−42.8990			−1.37246			−0.686230	+	0.727385i	$0.740736\pi$
$978$	−60.5163	−	60.5163i	−1.93510	−	1.93510i
$979$	−8.55311	+	25.0571i	−0.273358	+	0.800827i
$980$		−	0.0773367i		−	0.00247043i
$981$	−16.8549			−0.538136
$982$	3.77786	+	3.77786i	0.120556	+	0.120556i
$983$	2.13400	−	2.13400i	0.0680640	−	0.0680640i	−0.672255	−	0.740319i	$-0.734674\pi$
$983$	2.13400	−	2.13400i	0.0680640	−	0.0680640i	0.740319	+	0.672255i	$0.234674\pi$
$984$	−4.39891	−	4.39891i	−0.140232	−	0.140232i
$985$			0.0280601i			0.000894069i
$986$	12.0723	−	12.0723i	0.384459	−	0.384459i
$987$	−19.4079	+	19.4079i	−0.617761	+	0.617761i
$988$	47.5513			1.51281
$989$			14.8449i			0.472040i
$990$	−0.100880	−	0.0344348i	−0.00320617	−	0.00109441i
$991$	36.3215			1.15379			0.576895	−	0.816818i	$-0.304264\pi$
$991$	36.3215			1.15379			0.576895	+	0.816818i	$0.304264\pi$
$992$		−	8.15186i		−	0.258822i
$993$	−36.6213	−	36.6213i	−1.16214	−	1.16214i
$994$	−51.1448	+	51.1448i	−1.62221	+	1.62221i
$995$			0.0666225i			0.00211207i
$996$		−	38.8577i		−	1.23125i
$997$	−11.9410	+	11.9410i	−0.378175	+	0.378175i	−0.870444	−	0.492268i	$-0.836168\pi$
$997$	−11.9410	+	11.9410i	−0.378175	+	0.378175i	0.492268	+	0.870444i	$0.336168\pi$
$998$		−	64.3168i		−	2.03591i
$999$	−16.2828	+	16.2828i	−0.515167	+	0.515167i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.f.a.538.7	✓	120
11.10	odd	2	inner	671.2.f.a.538.54	yes	120
61.11	odd	4	inner	671.2.f.a.560.54	yes	120
671.560	even	4	inner	671.2.f.a.560.7	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.f.a.538.7	✓	120	1.1	even	1	trivial
671.2.f.a.538.54	yes	120	11.10	odd	2	inner
671.2.f.a.560.7	yes	120	671.560	even	4	inner
671.2.f.a.560.54	yes	120	61.11	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.70917 - 1.70917i) q^{2} +2.11174i q^{3} +3.84252i q^{4} -0.00911084i q^{5} +(3.60931 - 3.60931i) q^{6} +(1.54773 + 1.54773i) q^{7} +(3.14918 - 3.14918i) q^{8} -1.45943 q^{9} +O(q^{10})\)	\(q+(-1.70917 - 1.70917i) q^{2} +2.11174i q^{3} +3.84252i q^{4} -0.00911084i q^{5} +(3.60931 - 3.60931i) q^{6} +(1.54773 + 1.54773i) q^{7} +(3.14918 - 3.14918i) q^{8} -1.45943 q^{9} +(-0.0155720 + 0.0155720i) q^{10} +(-1.46186 - 2.97707i) q^{11} -8.11439 q^{12} -5.36148i q^{13} -5.29066i q^{14} +0.0192397 q^{15} -3.07992 q^{16} +(2.25034 - 2.25034i) q^{17} +(2.49441 + 2.49441i) q^{18} +2.30814 q^{19} +0.0350086 q^{20} +(-3.26839 + 3.26839i) q^{21} +(-2.58975 + 7.58689i) q^{22} +(1.24729 - 1.24729i) q^{23} +(6.65024 + 6.65024i) q^{24} +4.99992 q^{25} +(-9.16367 + 9.16367i) q^{26} +3.25328i q^{27} +(-5.94717 + 5.94717i) q^{28} +(-1.56937 + 1.56937i) q^{29} +(-0.0328839 - 0.0328839i) q^{30} +(3.94096 + 3.94096i) q^{31} +(-1.03425 - 1.03425i) q^{32} +(6.28679 - 3.08707i) q^{33} -7.69243 q^{34} +(0.0141011 - 0.0141011i) q^{35} -5.60788i q^{36} +(5.00505 + 5.00505i) q^{37} +(-3.94500 - 3.94500i) q^{38} +11.3220 q^{39} +(-0.0286917 - 0.0286917i) q^{40} -0.661466 q^{41} +11.1725 q^{42} +(-5.95086 + 5.95086i) q^{43} +(11.4395 - 5.61724i) q^{44} +0.0132966i q^{45} -4.26366 q^{46} +5.93807 q^{47} -6.50399i q^{48} -2.20908i q^{49} +(-8.54571 - 8.54571i) q^{50} +(4.75213 + 4.75213i) q^{51} +20.6016 q^{52} +(3.95947 - 3.95947i) q^{53} +(5.56041 - 5.56041i) q^{54} +(-0.0271236 + 0.0133188i) q^{55} +9.74815 q^{56} +4.87417i q^{57} +5.36463 q^{58} +(6.86132 + 6.86132i) q^{59} +0.0739289i q^{60} +(2.57724 + 7.37278i) q^{61} -13.4715i q^{62} +(-2.25879 - 2.25879i) q^{63} +9.69526i q^{64} -0.0488475 q^{65} +(-16.0215 - 5.46886i) q^{66} +(0.626356 + 0.626356i) q^{67} +(8.64699 + 8.64699i) q^{68} +(2.63394 + 2.63394i) q^{69} -0.0482023 q^{70} +(-9.66700 - 9.66700i) q^{71} +(-4.59600 + 4.59600i) q^{72} -7.48470i q^{73} -17.1090i q^{74} +10.5585i q^{75} +8.86906i q^{76} +(2.34513 - 6.87026i) q^{77} +(-19.3513 - 19.3513i) q^{78} +(-0.541000 - 0.541000i) q^{79} +0.0280607i q^{80} -11.2484 q^{81} +(1.13056 + 1.13056i) q^{82} +4.78874i q^{83} +(-12.5589 - 12.5589i) q^{84} +(-0.0205025 - 0.0205025i) q^{85} +20.3420 q^{86} +(-3.31409 - 3.31409i) q^{87} +(-13.9790 - 4.77167i) q^{88} +(-5.64484 - 5.64484i) q^{89} +(0.0227261 - 0.0227261i) q^{90} +(8.29811 - 8.29811i) q^{91} +(4.79273 + 4.79273i) q^{92} +(-8.32227 + 8.32227i) q^{93} +(-10.1492 - 10.1492i) q^{94} -0.0210290i q^{95} +(2.18406 - 2.18406i) q^{96} -4.16558i q^{97} +(-3.77569 + 3.77569i) q^{98} +(2.13348 + 4.34482i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 120 q^{9}+O(q^{10}) \) 120 * q - 120 * q^9	\( 120 q - 120 q^{9} - 4 q^{11} + 16 q^{12} + 16 q^{15} - 148 q^{16} + 56 q^{20} - 4 q^{22} - 4 q^{23} - 104 q^{25} + 40 q^{26} - 2 q^{33} - 8 q^{34} - 12 q^{37} + 20 q^{38} + 16 q^{42} - 10 q^{44} - 4 q^{53} + 50 q^{55} - 24 q^{56} + 64 q^{58} - 56 q^{67} + 68 q^{69} + 144 q^{70} - 12 q^{71} - 64 q^{77} + 84 q^{78} + 72 q^{81} + 40 q^{82} - 80 q^{86} + 4 q^{89} - 4 q^{91} + 4 q^{92} + 64 q^{93} + 24 q^{99}+O(q^{100}) \) 120 * q - 120 * q^9 - 4 * q^11 + 16 * q^12 + 16 * q^15 - 148 * q^16 + 56 * q^20 - 4 * q^22 - 4 * q^23 - 104 * q^25 + 40 * q^26 - 2 * q^33 - 8 * q^34 - 12 * q^37 + 20 * q^38 + 16 * q^42 - 10 * q^44 - 4 * q^53 + 50 * q^55 - 24 * q^56 + 64 * q^58 - 56 * q^67 + 68 * q^69 + 144 * q^70 - 12 * q^71 - 64 * q^77 + 84 * q^78 + 72 * q^81 + 40 * q^82 - 80 * q^86 + 4 * q^89 - 4 * q^91 + 4 * q^92 + 64 * q^93 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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